package leetcode.pre50;

import java.util.HashMap;

/**
 * 判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。
 *
 * 数字 1-9 在每一行只能出现一次。
 * 数字 1-9 在每一列只能出现一次。
 * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。
 *
 *
 * 上图是一个部分填充的有效的数独。
 *
 * 数独部分空格内已填入了数字，空白格用 '.' 表示。
 *
 * 示例 1:
 *
 * 输入:
 * [
 *   ["5","3",".",".","7",".",".",".","."],
 *   ["6",".",".","1","9","5",".",".","."],
 *   [".","9","8",".",".",".",".","6","."],
 *   ["8",".",".",".","6",".",".",".","3"],
 *   ["4",".",".","8",".","3",".",".","1"],
 *   ["7",".",".",".","2",".",".",".","6"],
 *   [".","6",".",".",".",".","2","8","."],
 *   [".",".",".","4","1","9",".",".","5"],
 *   [".",".",".",".","8",".",".","7","9"]
 * ]
 * 输出: true
 * 示例 2:
 *
 * 输入:
 * [
 *   ["8","3",".",".","7",".",".",".","."],
 *   ["6",".",".","1","9","5",".",".","."],
 *   [".","9","8",".",".",".",".","6","."],
 *   ["8",".",".",".","6",".",".",".","3"],
 *   ["4",".",".","8",".","3",".",".","1"],
 *   ["7",".",".",".","2",".",".",".","6"],
 *   [".","6",".",".",".",".","2","8","."],
 *   [".",".",".","4","1","9",".",".","5"],
 *   [".",".",".",".","8",".",".","7","9"]
 * ]
 * 输出: false
 * 解释: 除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。
 *      但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。
 * 说明:
 *
 * 一个有效的数独（部分已被填充）不一定是可解的。
 * 只需要根据以上规则，验证已经填入的数字是否有效即可。
 * 给定数独序列只包含数字 1-9 和字符 '.' 。
 * 给定数独永远是 9x9 形式的。
 *
 * 来源：力扣（LeetCode）
 * 链接：https://leetcode-cn.com/problems/valid-sudoku
 * 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
 *
 *
 * 一个简单的解决方案是遍历该 9 x 9 数独 三 次，以确保：
 *
 * 行中没有重复的数字。
 * 列中没有重复的数字。
 * 3 x 3 子数独内没有重复的数字。
 * 实际上，所有这一切都可以在一次迭代中完成。
 *
 * 作者：LeetCode
 * 链接：https://leetcode-cn.com/problems/valid-sudoku/solution/you-xiao-de-shu-du-by-leetcode/
 * 来源：力扣（LeetCode）
 * 著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
 */
class Code36_IsValidSudoku_有效数独 {
    public boolean isValidSudoku(char[][] board) {
        //每行中是否有重复的
        HashMap<Integer, Integer>[] rows = new HashMap[9];
        //每列中是否有重复的
        HashMap<Integer, Integer>[] columns = new HashMap[9];
        //9个块状中是否有重复的
        HashMap<Integer, Integer>[] boxes = new HashMap[9];

        for (int i = 0; i < 9; i++) {
            rows[i] = new HashMap<>();
            columns[i] = new HashMap<>();
            boxes[i] = new HashMap<>();
        }

        // validate a board
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char num = board[i][j];
                if (num != '.') {
                    int n = (int) num;
                    /**
                     * 注意块状索引算法。
                     * 前三行 0 1 2
                     * 中间三行 3 4 5
                     * 最后三行 6 7 8
                     *
                     * 行每隔3行+3，列每隔3行+1
                     * index = (i/3)*3 + j/3
                     *
                     */

                    int box_index = (i / 3) * 3 + j / 3;

                    // keep the current cell value
                    rows[i].put(n, rows[i].getOrDefault(n, 0) + 1);
                    columns[j].put(n, columns[j].getOrDefault(n, 0) + 1);
                    boxes[box_index].put(n, boxes[box_index].getOrDefault(n, 0) + 1);

                    // check if this value has been already seen before
                    if (rows[i].get(n) > 1 || columns[j].get(n) > 1 || boxes[box_index].get(n) > 1)
                        return false;
                }
            }
        }

        return true;
    }
}